# Find the domain and range of each of the relations given below:

Question:

Find the domain and range of each of the relations given below:

(i) $R=\{(-1,1),(1,1),(-2,4),(2,4),(2,4),(3,9)\}$

(ii) $\mathrm{R}=\left\{\left(\mathrm{x}, \frac{1}{\mathrm{x}}\right): \mathrm{x}\right.$ is an interger, $\left.0<\mathrm{x}<5\right\}$

(iii) $R=\{(x, y): x+2 y=8$ and $x, y \in N\}$

(iv) $R=\{(x, y),: y=|x-1|, x \in Z$ and $|x| \leq 3\}$

Solution:

(i) Given: $R=\{(-1,1),(1,1),(-2,4),(2,4),(2,4),(3,9)\}$

$\operatorname{Dom}(R)=\{x:(x, y) \in R\}=\{-2,-1,1,2,3\}$

Range $(R)=\{y:(x, y) \in R\}=\{1,4,9\}$

(ii) Given:

$R=\left\{\left(x, \frac{1}{x}\right): x\right.$ is an interger, $\left.0 That means,$R=\left\{(1,1),\left(2, \frac{1}{2}\right),\left(3, \frac{1}{3}\right),\left(4, \frac{1}{4}\right)\right\}\operatorname{Dom}(R)=\left\{x:(x, y)^{\in} R\right\}=\{1,2,3,4\}$Range$(R)=\left\{y:(x, y) \in_{R}\right\}=\left\{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$(iii) Given:$\mathrm{R}=\{(\mathrm{x}, \mathrm{y}): \mathrm{x}+2 \mathrm{y}=8$and$\mathrm{x}, \mathrm{y} \in \mathrm{N}\}$That means,$R=\{(2,3),(4,2),(6,1)\}\operatorname{Dom}(R)=\{x:(x, y) \in R\}=\{2,4,6\}$Range$(R)=\left\{y:(x, y)^{\in} R\right\}=\{1,2,3\}$(iv) Given:$R=\{(x, y): y=|x-1|, x \in Z$and$|x| \leq 3\}\operatorname{Dom}(R)=\left\{x:(x, y)^{\in} R\right\}=\{-3,-2,-1,0,1,2,3\}$Range$(R)=\left\{y:(x, y)^{\in} R\right\}=\{0,1,2,3,4\}\$